ek_solutions-1

# ek_solutions-1 - Solutions to the Practice Problems on the...

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Unformatted text preview: Solutions to the Practice Problems on the Relationship between Kinetics and Equilibrium 1. The rate of production of C (for instance) is 1 ¥ k £ ¤¡ ¡ ¢ ¦ ¡ ¦  10  ¡ ¥ 12 k 18 s 1 ¦ 1 ¥ ¦ ¢ ¥ ¥ ¢  ¨  ¥ ¢ ¨ ©¡ ¥ ¡ ¢ ¡ ¦ ¢ ¦ ¡ 1 ¥ ¢ k 1C k1 K k1 k1 1 4 10 3 L mol 1 s K 1 2 1015 L mol C ¦ §¡ ¡ ¢ ¥ ¡  ¡  (a) A and B are reactants. C is an intermediate. D is a product. D ¡ ¡ D ¡ 0. From dB dt 0, we ¢ ¢ ¢ ! £ ¡ ¡ ¢ ¡ ¢ ¡ ¡ ¢ ¡ ¡ ¢ ¡ (1) ¦ ¥ ¢ ¡ ¡ ¥ ¢ "¡ ¡ ¡ 0, we get the additional condition k 2D k2 k2 ¦ ¥ ¥ ¢ ¢ ¡ ¡ ¡ ¡ ¡ 1 k2 A C D or AC ¡ ¢ ! dD dt k1 k1 dD dt ! ¥ £ ¡ From 2 ! ¥ £ ¤¡ £ C AB  ¡ £ ¡ B (d) At equilibrium, all of the rates vanish. In particular, ddt get k1 A B k 1 C from which it follows that k ¥ k2 A C D ¡  ¡ D ¥  ¡ 2 ¥ C 2 £ ¡ 1 k k C ¡ ¡ k2 A C 1 k2 A C ¥ k1 A B k C 1 ¡ k1 A B k k1 A B dA dt dB dt dC dt dD dt B (c)  (b) 2A  2. k k1 A B C AB 0 so At equilibrium, d C dt k1 A B dC dt (2) The equilibrium constant for the overall reaction is ¡ A2B ¦ D ¡ ¡ K ¢ ¢ #¡ ¦ AB k1 k2 k 1k 2 k1 k2 k 1k 2 ¥ ¥ ¡ ¡ ¥ ¢ ¡ ¢ 2 2 ¥ K D ¡ C D AB AC ¦ If we multiply equations 1 and 2 together, we get ¡  ¡ ¡ ¡ ...
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